![]() ![]() The use of computer arithmetic and thus the introduction of roundoff errors adds another dimension of inaccuracy to the MATLAB based analysis. It is quite feasible when dealing with smaller systems but becomes unscalable for larger systems, as managing breakpoints and deciding their suitable positions to ensure that the whole range of possible values is covered becomes extremely difficult. Similarly, the breakpoints based approach tests the behavior of the given program by inserting breakpoints at various discrete steps only. Simulation and testing do not guarantee a complete analysis, since the system under test is simulated for a specific set of inputs and at specified intervals of time. Some testing frameworks ( ) are also used to partially test the MATLAB code by providing a subset of all possible input combinations. Traditionally, the Simulink models are validated through simulation, and the m-code based models are analyzed through debugging, that is, by setting breakpoints at different levels and examining the values of outputs/variables. Generally, model-based systems are represented in Simulink ( ), while algorithms are expressed using m-code in MATLAB based analysis of systems. One of the prime motivations of its widespread usage is the availability of a collection of built-in functions based on basic matrix operations, which can be built upon for developing a library of larger, more complex, functions. MATLAB ( ) (MATrix-LABoratory) is arguably one of the most commonly used software environments for modeling and analyzing complex systems in various domains of engineering and science, including analog and mixed signal circuits, digital filters and control systems. For illustrating the usefulness of the proposed library and approach, we present the formal analysis of a Finite Impulse Response (FIR) filter, which is quite commonly used in digital signal processing applications, within the sound core of the HOL Light theorem prover. The formal models can then be formally verified in an interactive theorem prover. To facilitate this process, we present a library of higher-order-logic functions corresponding to the commonly used matrix functions of MATLAB as well as a translator that allows automatic conversion of MATLAB models to higher-order logic. ![]() Formal verification can overcome these limitations, but developing the formal models of the underlying MATLAB models is a very challenging and time-consuming task, especially in the case of higher-order-logic models. These methods provide limited coverage due to their inherent incompleteness. Traditionally, the analysis of MATLAB models is done using simulation and debugging/testing frameworks. MATLAB is a software based analysis environment that supports a high-level programing language and is widely used to model and analyze systems in various domains of engineering and sciences. ![]()
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